Mini Lesson Question
Question #2: Interpret Linear Functions
Interpret Linear Functions
A linear function is a function that represents a line on the coordinate plane. A line can be written in slope-intercept form, , where is the slope and is the -intercept. The dependent variable is , and the independent variable is . The can be replaced by , so the function can be written as .
Andrei wants to fill a glass tank with marbles, each with the same volume, and then fill the remaining space with water. The function represents the volume of water, in liters, Andrei uses if he uses marbles.
You can rewrite the function in slope-intercept form: . The slope is –0.05, and the -intercept is 32.
What is the volume of the tank?
represents the volume left in the tank after marbles were added. The volume of the tank is the initial volume before any of the marbles have been added, or . . The volume of the tank is 32 liters.
What is the volume of each marble?
The volume of water needed to fill the tank decreases by 0.05 liters each time Andrei puts in a marble, . This means that the volume of each marble is 0.05 liters.
Try it
Try It: Interpret Linear Functions
Rachel is a stunt driver, and she is escaping from a building that is about to explode. The function represents the remaining distance, , in meters after seconds.
How long is the distance Rachel has to drive?
Compare your answers:
Here is how to interpret linear functions:
The function represents the remaining distance, , in meters after seconds. The total distance she must travel is the initial value, or . . The total distance she must travel is 220 meters.
Check Your Understanding
The amount of money that farmers in Massachusetts paid to maintain their crops between 1991 and 2008 is modeled by the function , where is the amount of money the farmers paid, in millions of dollars, and is the year (with 1991 as ). What does the 3.53 mean in the equation?
Multiple Choice:
The costs for maintaining crops increased by $3.53 million each year between 1991 and 2008.
The costs for maintaining crops increased a total of $3.53 million between 1991 and 2008.
The costs for maintaining crops was $3.53 million in 1991.
The costs for maintaining crops was $3.53 million in 2008.
Check yourself: 3.53 is the rate of increase each year.
Videos: Interpreting Linear Functions
Khan Academy: Interpret Linear Functions
Watch the videos to see how to interpret a linear function.